Beta Cells: One of our main activities over the last few years has been the development of a comprehensive model for oscillations of membrane potential and calcium on time scales ranging from seconds to minutes. These lead to corresponding oscillations of insulin secretion. The basic hypothesis of the model is that the faster oscillations (tens of seconds) stem from feedback of calcium onto ion channels, likely calcium-activated potassium (K(Ca)) channels and ATP-dependent potassium (K(ATP)) channels, whereas the slower oscillations (five minutes) stem from oscillations in metabolism. The metabolic oscillations are transduced into electrical oscillations via the K(ATP) channels. The model thus consists of an electrical oscillator (EO) and a metabolic oscillator (MO) and is referred to as the Dual Oscillator Model (DOM). In our model, the MO is a glycolytic oscillator, but many of the features of the system would still hold if the metabolic oscillation arose elsewhere, such as the mitochondria. K(ATP) channels are of clinical significance as they are a first-line target of insulin-stimulating drugs, such as the sulfonylureas tolbutamide and glyburide, used in the treatment of Type 2 Diabetes. Severe gain-of-function mutations of K(ATP) are a major cause of neo-natal diabetes mellitus, whereas moderate gain-of-function mutations have been linked in genome-wide association studies (GWAS) to the milder but more common disease, adult-onset type 2 diabetes. Conversely, loss-of-function mutations of K(ATP) are a major cause of familial hyperinsulinism, a hereditary disease found in children in which beta cells are persistently electrically active and secrete insulin in the face of normal or low glucose, causing life-threatening hypoglycemia. For a review of the importance of oscillations of insulin secretion for health and disease see Reference # 3 in the 2015 report. Over a period of years we have accumulated a good deal of indirect evidence supporting the model, but we felt it important to devise a direct test of the central feature, namely that glycolysis oscillates. Our experimental collaborators developed a FRET-based sensor by modifiying pyruvate kinase (PK). PK binds fructose-1,6-bisphosphate (FBP), a key glycolytic metabolite, which was predicted to oscillate by the DOM. A previous paper confirmed that the sensor (PKAR, for pyruvate kinase activity reporter) does oscillate. In the current period the characteristics of the oscillations were probed more stringently by recording them simultaneously with membrane potential in order to ascertain the phase relationship between them. The experiments (Ref. # 1) again confirmed that PKAR oscillates and that it can do so even when calcium does not oscillate, as also predicted by the model. However, the phase relationship did not agree with the model prediction: PKAR declined during the active phase of the oscillation, whereas it was predicted to be high throughout the active phase because of a pulse of glycolytic activity. Two other metabolites, NAD(P)H and ATP, were also imaged and revealed a similar pattern. The discrepancy between prediction and experiment was striking but required only one major revision to the model to resolve. A previously known but neglected effect of calcium to accelerate the citric acid was added. This increases mitochondrial consumption of pyruvate, drawing down cytosolic FBP rapidly enough to overcome the surge in FBP production in glycolysis. In order to match the observation that ATP also declined during the active phase, it was necessary to assume in addition that the consumption of ATP by calcium pumps during the active phase was great enough to overcome the increased ATP production due to the stimulation of the citric acid cycle. This potent consumption of ATP serves to hasten the termination of the active phase because it allows K(ATP) channels to reopen. Further work will be needed to test the new predictions generated by the revised model and to fully understand the benefits of this more complicated arrangement. Alpha Cells: The regulation of glucagon secretion in the pancreatic -cell is not well understood. It has been proposed that glucose suppresses glucagon secretion either directly through an intrinsic mechanism, within the -cell, or indirectly through an extrinsic mechanism. We previously described a mathematical model for isolated pancreatic alpha-cells and used it to investigate possible intrinsic mechanisms of regulating glucagon secretion. We demonstrated that glucose can suppress glucagon secretion through both ATP-dependent potassium channels (K(ATP)) and a store-operated current (SOC). We now develop an islet model that combines previously published mathematical models of alpha- and beta-cells with a new model of delta-cells and use it to explore the effects of insulin and somatostatin on glucagon secretion. We show that the model can reproduce experimental observations that the inhibitory effect of glucose remains even when paracrine modulators are no longer acting on the -cell. We demonstrate how paracrine interactions can either synchronize - and -cells to produce pulsatile oscillations in glucagon and somatostatin secretion or fail to do so. The model can also account for the paradoxical observation that glucagon can be out of phase with insulin while alpha-cell calcium is in phase with insulin. We conclude that both paracrine interactions and the alpha-cell's intrinsic mechanisms are needed to explain the response of glucagon secretion to glucose.